Watson has been in excellent form on the grass and she continued that in a 6-0 6-4 victory over the Latvian.
The opening set saw the British number two produce arguably her best tennis all year as she dismantled Sevastova, registering three successive breaks to wrap up a bagel set in just 19 minutes.
Sevastova stopped the rot in the second and moved into a 3-1 lead with a break of her own but there was no stopping Watson, who played the kind of aggressive tennis which helped her reach the semi-finals of the Eastbourne Invitational last week.
Watson ended the match with three successive breaks of serve to book her place in the last 32 in just 61 minutes.
She will now face former world number one Victoria Azarenka, who is making her first appearance at a Grand Slam tournament since the birth of her first child.